Combining Texts

All the ideas for 'Must We Believe in Set Theory?st1=George Boolos', 'The Art of the Infinite' and 'Mind and Body'

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31 ideas

4. Formal Logic / F. Set Theory ST / 1. Set Theory
10482 The logic of ZF is classical first-order predicate logic with identity [Boolos]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / a. Axioms for sets
10492 A few axioms of set theory 'force themselves on us', but most of them don't [Boolos]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / j. Axiom of Choice IX
15717 Using Choice, you can cut up a small ball and make an enormous one from the pieces [Kaplan/Kaplan]
4. Formal Logic / F. Set Theory ST / 5. Conceptions of Set / d. Naïve logical sets
10485 Naïve sets are inconsistent: there is no set for things that do not belong to themselves [Boolos]
4. Formal Logic / F. Set Theory ST / 5. Conceptions of Set / e. Iterative sets
10484 The iterative conception says sets are formed at stages; some are 'earlier', and must be formed first [Boolos]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / b. Types of number
15712 1 and 0, then add for naturals, subtract for negatives, divide for rationals, take roots for irrationals [Kaplan/Kaplan]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / g. Real numbers
15711 The rationals are everywhere - the irrationals are everywhere else [Kaplan/Kaplan]
6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / f. Arithmetic
15714 'Commutative' laws say order makes no difference; 'associative' laws say groupings make no difference [Kaplan/Kaplan]
15715 'Distributive' laws say if you add then multiply, or multiply then add, you get the same result [Kaplan/Kaplan]
6. Mathematics / A. Nature of Mathematics / 5. The Infinite / a. The Infinite
10491 Infinite natural numbers is as obvious as infinite sentences in English [Boolos]
6. Mathematics / A. Nature of Mathematics / 5. The Infinite / f. Uncountable infinities
10483 Mathematics and science do not require very high orders of infinity [Boolos]
6. Mathematics / C. Sources of Mathematics / 1. Mathematical Platonism / a. For mathematical platonism
10490 Mathematics isn't surprising, given that we experience many objects as abstract [Boolos]
7. Existence / C. Structure of Existence / 2. Reduction
4986 A weaker kind of reductionism than direct translation is the use of 'bridge laws' [Kirk,R]
8. Modes of Existence / D. Universals / 1. Universals
10488 It is lunacy to think we only see ink-marks, and not word-types [Boolos]
9. Objects / A. Existence of Objects / 2. Abstract Objects / a. Nature of abstracta
10487 I am a fan of abstract objects, and confident of their existence [Boolos]
9. Objects / A. Existence of Objects / 2. Abstract Objects / c. Modern abstracta
10489 We deal with abstract objects all the time: software, poems, mistakes, triangles.. [Boolos]
14. Science / C. Induction / 3. Limits of Induction
15713 The first million numbers confirm that no number is greater than a million [Kaplan/Kaplan]
15. Nature of Minds / B. Features of Minds / 1. Consciousness / c. Parts of consciousness
5001 Maybe we should see intentionality and consciousness as a single problem, not two [Kirk,R]
15. Nature of Minds / B. Features of Minds / 4. Intentionality / a. Nature of intentionality
4993 If a bird captures a worm, we could say its behaviour is 'about' the worm [Kirk,R]
15. Nature of Minds / B. Features of Minds / 4. Intentionality / b. Intentionality theories
5000 Behaviourism says intentionality is an external relation; language of thought says it's internal [Kirk,R]
17. Mind and Body / A. Mind-Body Dualism / 8. Dualism of Mind Critique
4982 Dualism implies some brain events with no physical cause, and others with no physical effect [Kirk,R]
17. Mind and Body / B. Behaviourism / 1. Behaviourism
4991 Behaviourism seems a good theory for intentional states, but bad for phenomenal ones [Kirk,R]
4994 Behaviourism offers a good alternative to simplistic unitary accounts of mental relationships [Kirk,R]
17. Mind and Body / B. Behaviourism / 2. Potential Behaviour
4992 In 'holistic' behaviourism we say a mental state is a complex of many dispositions [Kirk,R]
17. Mind and Body / B. Behaviourism / 4. Behaviourism Critique
4990 The inverted spectrum idea is often regarded as an objection to behaviourism [Kirk,R]
17. Mind and Body / E. Mind as Physical / 3. Eliminativism
4984 All meaningful psychological statements can be translated into physics [Kirk,R]
17. Mind and Body / E. Mind as Physical / 4. Connectionism
4998 Instead of representation by sentences, it can be by a distribution of connectionist strengths [Kirk,R]
17. Mind and Body / E. Mind as Physical / 7. Anti-Physicalism / b. Multiple realisability
4985 If mental states are multiply realisable, they could not be translated into physical terms [Kirk,R]
18. Thought / D. Concepts / 2. Origin of Concepts / c. Nativist concepts
4997 It seems unlikely that most concepts are innate, if a theory must be understood to grasp them [Kirk,R]
19. Language / A. Nature of Meaning / 5. Meaning as Verification
4999 For behaviourists language is just a special kind of behaviour [Kirk,R]
19. Language / B. Reference / 1. Reference theories
4995 Behaviourists doubt whether reference is a single type of relation [Kirk,R]